Looks good. The if is a bit shaky, and I don't mean the one you think:

if ($possible) {
  $average = sprintf("%2.2f", ($earned / $possible) * 100);

  if    ($average >= 95) { $grade = "A";  }
  elsif ($average >= 90) { $grade = "A-"; }
  elsif ($average >= 87) { $grade = "B+"; }
  elsif ($average >= 84) { $grade = "B";  }
  elsif ($average >= 80) { $grade = "B-"; }
  elsif ($average >= 77) { $grade = "C+"; }
  elsif ($average >= 74) { $grade = "C";  }
  elsif ($average >= 70) { $grade = "C-"; }
  elsif ($average >= 67) { $grade = "D+"; }
  elsif ($average >= 64) { $grade = "D";  }
  elsif ($average >= 60) { $grade = "D-"; }
  elsif ($average <  60) { $grade = "E";  }

} else {

  $grade = $average = $earned = $possible = "?";
}
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One way to get rid of the big if:

@GRADES   = qw( E  D- D  D+ C- C  C+ B- B  B+ A- A  );
@BRACKETS =   (    60,64,67,70,74,77,80,84,87,90,95 );


if ($possible) {
  $average = sprintf("%2.2f", ($earned / $possible) * 100);

  $grade = 0;
  foreach (@BRACKETS) { $grade++ if ($average >= $_); }
  $grade = $GRADES[$grade];

} else {

  $grade = $average = $earned = $possible = "?";
}
[download]

And how about only preparing the query only once:

# prepare query
$cursor = $dbh->prepare('SELECT * FROM grades WHERE className=?');

# cycle through courses
foreach $course (@courses) {

  # execute query
  $cursor->execute($course);

  ...
}

...
[download]